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The CH2+ cation
Volume 141, number 6
CHEMICAL PHYSICS LETTERS
27 November 1987
THE CH” CATION R. FRIEDMAN ‘, S. PRESTON 2 and A. DALGARNO Harvard-Smithsonian
Centerfor Astrophysics, Cambridge, MA 02138, USA
Received 19 July 1987; in final form 13 October 1987
A tentative identification is proposed of the state of CH*+ which has been detected in energy loss experiments with a lifetime of at least 3 ks. An empirical modification of a calculated potential energy curve is made which yields a well about I eV deep in the repulsive curve of the ground electronic state near I .2 1A. An elastic scattering resonance level occurs at the measured excitation energy and has a width corresponding to a lifetime of 3.2 IS.
1. Introduction Mathur et al. [ 1 ] and Mathur and Badrinathan [ 21 have carried out measurements of translational energy loss of the products of collisions of hydrocarbon ions CHZ (n= 1-5) with Kr, CH,, and Nz. In the experiments, doubly charged ions CHi+ are created which are stable towards unimolecular dissociation for times of the order of 3 ps. The identification of the molecular states of the doubly charged ions is uncertain. Calculations of the adiabatic potential energy curves of the ground and excited electronic states of the diatomic molecular ion CH*+ have been reported [3-51 and the couplings between the adiabatic states for the radial components of the nuclear momentum have been obtained [ 41. We explore here the identity of the molecular ion CH2+ which has a lifetime of at least 3 p.s.
2. The CH*+cation Multicharged molecular ions have excited states which separate to a neutral atom or molecule and a multicharged ionic species. The polarization attraction produces a potential well that pay be deep enough to support bound levels. The well may be amplified by interactions with neighbouring elec’ Also at Department of Chemistry, Harvard University, Cambridge, MA, USA. ’ Now at Lincoln Laboratories, Lexington, MA, USA.
tronic states which separate to a pair of charged species; however if these latter states are lower in energy at large internuclear distances, they cause predissociation of the bound levels [ 61. The molecular states are those participating in charge transfer processes [ 4,7]. Some of the quasi-discrete vibrational levels may predissociate slowly but they can decay also by the emission of radiation to the lower lying repulsive electronic states in times much shorter than the minimum lifetime of 3 ys required for the detection of doubly charged molecular ions in the energy loss experiments. It seems therefore that the CH2+ ion that is detected must be in its lowest electronic state. An early study [ 31 concluded that the ground state is wholly repulsive but the more elaborate calculations of Heil, Butler and Dalgamo [ 41 showed that the interaction of the ground state (which is of the C+---H+ type) with the excited 2 2Z+ state (which is of the C2+---H type) induced a shallow dip in the repulsive curve at small internuclear distances. A similar result was found by Wetmore, Boyd and LeRoy [ 51. From the measured onset energy, Mathur and Badrinathan [ 21 inferred a value of 33.74 -t 0.20 eV for the energy required for the double ionization of CH. In the calculations of Wetmore et al. [ 51 the shallow dip occurs at an energy of 34 eV above the ground state of CH in apparent agreement with the experimental data. However as Mathur and Badrinathan [ 21 point out, the internuclear distance of 1S 8, obtained by Wetmore et al. [ 51 for the weak minimum compared to the equilibrium separation 469
Volume I4 1, number 6
CHEMICAL PHYSICS LETTERS 0.36
11
“1
“‘I
I”’
1
I ”
”
27 November 1987
I””
l
’ ”
l
”
-ADIABATIC
”
1
’
STATE i
INTERNUCLEAR
DISTANCE
( oo)
Fig. 1. The adiabatic potential energy curve of the ground state of CH’+. The crosses x are the calculations of ref. [ 41. The point + is selected to create a resonance state with a predissociation lifetime of 3 us.
‘t
0
I -5
I -4
I -3
I
I
I
I
I
I
I
I
-2
-I
0
I
2
3
4
5
E- ERES ( IO-” a.u.)
Fig. 2. The profile of the ratio of the resonance scattering cross section uRESto the background cross section ueoK as a function of the energy E around the resonance energy ERES
470
Volume 14 1, number 6
CHEMICAL PHYSICS LETTERS
of 1.13 8, for the ground state of CH+ makes it unlikely that the level would be populated from the ground vibrational state. If excitation occurs from vibrationally excited states of CH+, the consistency between the measured and theoretical energies is lost. The calculations of Heil et al. [4] provide better agreement; they yield a vertical energy of 34.3 eV at an internuclear distance of 1.2 A. Neither of the theoretical potential energy curves of the ground electronic state contains a well deep enough to retain a quasi-discrete level against predissociation through the barrier for a time approaching 3 us but the proximity of the minimum in energy and internuclear separation to the experimental observations suggests nevertheless that the ground electronic state is responsible. We have explored the changes to the potential energy curve that would lead to a quasi-discrete vibrational level with a lifetime towards predissociation on the order of 1 ps. Because the shallow dip is caused by an electronic interaction with the excited 2 ‘C + state, we included its coupling to the ground 1 2C+ state arising from the radial component of the nuclear kinetic energy operator which had been calculated previously [ 41 in an investigation of the charge transfer of C2+ with H. We solved the coupled equations for elastic scattering in the 1 2Z + channel at energies at which the 2 ‘C + channel is closed and we conducted a numerical search for the elastic scattering resonances. Initial estimates of their locations were obtained by transforming the uncoupled equation for the open channel to that for a closed channel by extending the barrier at 2.7 a, in the 1 2C+ potential out to an infinite internuclear distance. The resonance energies were only slightly shifted from the discrete energy levels of the modified potential. The resonances are the quasi-discrete levels and their widths determine their lifetimes [ 61. Fig. 1 shows the original computed points of the adiabatic potential energy curve for the 1 *X+ state of CH2+ (41. We added a single point at 2.285 a0 and moved it down in energy. The points were used to generate spline fits to the potential energy curve. The potential curve of the 2 ‘C + state and the adiabatic coupling matrix elements were left unaltered. In practice, the coupling effects were unimportant and although we employed a two-state formulation,
27 November 1987
a single channel adiabatic description would have sufficed. We found that by inserting a point at an energy of 0.1885 au above the C+ (2P) +H+ asymptotic limit and generating the potential energy curve shown by the solid line in fig. 1, we created a scattering resonance with a width corresponding to a dissociation lifetime of 3.2 l.~s.The resonance is shown in fig. 2 where the ratio of the cross section to the background cross section is fitted by a Fano profile with and a width of a shape parameter q=-2.8438 7.549 x lo- I2au at a resonance energy of 0.2056 au. The double ionization energy is 33.92 eV compared to the measured value of 33.74 f 0.20 eV. The curve could be deepened slightly with a corresponding increase in the lifetime of the level and remain consistent with the measurements. A semi-classical analysis indicated that the empirical potential that we constructed may contain two resonances and indeed we located a second at an energy of 0.2333 au, just below the edge of the barrier, with a width corresponding to a lifetime of 2 x lo-l4 S.
Relined quanta1 calculations of the potential energy curve of the lowest ‘C + state of CH2+ are needed to confirm or reject our tentative identification of the doubly charged CH*+ ion observed by Mathur et al. [1,2]. Acknowledgement This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences. References [ I] D. Mathur, C. Badrinathan, F.A. Rajgara and U.T. Raheja, Chem. Phys. 103 (1986) 447.
[ 21 D. Mathur and C. Badrinathan, J. Phys. B20 (1987) 15 17. [3] J.A. Pople, B. Tidor and P. von R. Schleyer, Chem. Phys. Letters 88 (1982) 533. [4] T.G. Heil, SE. Butler and A. Dalgamo, Phys. Rev. A27 (1983) 2365. [ 5 I R.W. wetmore,R.K. Boyd and R.J. LeRoy, Chem. Phys. 89 (1984) 329. 161s. PrestonandA.Dalgamo,Chem.Phys. Letters 138 (1987) 157. [7] T.G. Heil, SE. Butler and A. Dalgamo, Phys. Rev. A 23 (1981) 1100.
471
CHEMICAL PHYSICS LETTERS
27 November 1987
THE CH” CATION R. FRIEDMAN ‘, S. PRESTON 2 and A. DALGARNO Harvard-Smithsonian
Centerfor Astrophysics, Cambridge, MA 02138, USA
Received 19 July 1987; in final form 13 October 1987
A tentative identification is proposed of the state of CH*+ which has been detected in energy loss experiments with a lifetime of at least 3 ks. An empirical modification of a calculated potential energy curve is made which yields a well about I eV deep in the repulsive curve of the ground electronic state near I .2 1A. An elastic scattering resonance level occurs at the measured excitation energy and has a width corresponding to a lifetime of 3.2 IS.
1. Introduction Mathur et al. [ 1 ] and Mathur and Badrinathan [ 21 have carried out measurements of translational energy loss of the products of collisions of hydrocarbon ions CHZ (n= 1-5) with Kr, CH,, and Nz. In the experiments, doubly charged ions CHi+ are created which are stable towards unimolecular dissociation for times of the order of 3 ps. The identification of the molecular states of the doubly charged ions is uncertain. Calculations of the adiabatic potential energy curves of the ground and excited electronic states of the diatomic molecular ion CH*+ have been reported [3-51 and the couplings between the adiabatic states for the radial components of the nuclear momentum have been obtained [ 41. We explore here the identity of the molecular ion CH2+ which has a lifetime of at least 3 p.s.
2. The CH*+cation Multicharged molecular ions have excited states which separate to a neutral atom or molecule and a multicharged ionic species. The polarization attraction produces a potential well that pay be deep enough to support bound levels. The well may be amplified by interactions with neighbouring elec’ Also at Department of Chemistry, Harvard University, Cambridge, MA, USA. ’ Now at Lincoln Laboratories, Lexington, MA, USA.
tronic states which separate to a pair of charged species; however if these latter states are lower in energy at large internuclear distances, they cause predissociation of the bound levels [ 61. The molecular states are those participating in charge transfer processes [ 4,7]. Some of the quasi-discrete vibrational levels may predissociate slowly but they can decay also by the emission of radiation to the lower lying repulsive electronic states in times much shorter than the minimum lifetime of 3 ys required for the detection of doubly charged molecular ions in the energy loss experiments. It seems therefore that the CH2+ ion that is detected must be in its lowest electronic state. An early study [ 31 concluded that the ground state is wholly repulsive but the more elaborate calculations of Heil, Butler and Dalgamo [ 41 showed that the interaction of the ground state (which is of the C+---H+ type) with the excited 2 2Z+ state (which is of the C2+---H type) induced a shallow dip in the repulsive curve at small internuclear distances. A similar result was found by Wetmore, Boyd and LeRoy [ 51. From the measured onset energy, Mathur and Badrinathan [ 21 inferred a value of 33.74 -t 0.20 eV for the energy required for the double ionization of CH. In the calculations of Wetmore et al. [ 51 the shallow dip occurs at an energy of 34 eV above the ground state of CH in apparent agreement with the experimental data. However as Mathur and Badrinathan [ 21 point out, the internuclear distance of 1S 8, obtained by Wetmore et al. [ 51 for the weak minimum compared to the equilibrium separation 469
Volume I4 1, number 6
CHEMICAL PHYSICS LETTERS 0.36
11
“1
“‘I
I”’
1
I ”
”
27 November 1987
I””
l
’ ”
l
”
-ADIABATIC
”
1
’
STATE i
INTERNUCLEAR
DISTANCE
( oo)
Fig. 1. The adiabatic potential energy curve of the ground state of CH’+. The crosses x are the calculations of ref. [ 41. The point + is selected to create a resonance state with a predissociation lifetime of 3 us.
‘t
0
I -5
I -4
I -3
I
I
I
I
I
I
I
I
-2
-I
0
I
2
3
4
5
E- ERES ( IO-” a.u.)
Fig. 2. The profile of the ratio of the resonance scattering cross section uRESto the background cross section ueoK as a function of the energy E around the resonance energy ERES
470
Volume 14 1, number 6
CHEMICAL PHYSICS LETTERS
of 1.13 8, for the ground state of CH+ makes it unlikely that the level would be populated from the ground vibrational state. If excitation occurs from vibrationally excited states of CH+, the consistency between the measured and theoretical energies is lost. The calculations of Heil et al. [4] provide better agreement; they yield a vertical energy of 34.3 eV at an internuclear distance of 1.2 A. Neither of the theoretical potential energy curves of the ground electronic state contains a well deep enough to retain a quasi-discrete level against predissociation through the barrier for a time approaching 3 us but the proximity of the minimum in energy and internuclear separation to the experimental observations suggests nevertheless that the ground electronic state is responsible. We have explored the changes to the potential energy curve that would lead to a quasi-discrete vibrational level with a lifetime towards predissociation on the order of 1 ps. Because the shallow dip is caused by an electronic interaction with the excited 2 ‘C + state, we included its coupling to the ground 1 2C+ state arising from the radial component of the nuclear kinetic energy operator which had been calculated previously [ 41 in an investigation of the charge transfer of C2+ with H. We solved the coupled equations for elastic scattering in the 1 2Z + channel at energies at which the 2 ‘C + channel is closed and we conducted a numerical search for the elastic scattering resonances. Initial estimates of their locations were obtained by transforming the uncoupled equation for the open channel to that for a closed channel by extending the barrier at 2.7 a, in the 1 2C+ potential out to an infinite internuclear distance. The resonance energies were only slightly shifted from the discrete energy levels of the modified potential. The resonances are the quasi-discrete levels and their widths determine their lifetimes [ 61. Fig. 1 shows the original computed points of the adiabatic potential energy curve for the 1 *X+ state of CH2+ (41. We added a single point at 2.285 a0 and moved it down in energy. The points were used to generate spline fits to the potential energy curve. The potential curve of the 2 ‘C + state and the adiabatic coupling matrix elements were left unaltered. In practice, the coupling effects were unimportant and although we employed a two-state formulation,
27 November 1987
a single channel adiabatic description would have sufficed. We found that by inserting a point at an energy of 0.1885 au above the C+ (2P) +H+ asymptotic limit and generating the potential energy curve shown by the solid line in fig. 1, we created a scattering resonance with a width corresponding to a dissociation lifetime of 3.2 l.~s.The resonance is shown in fig. 2 where the ratio of the cross section to the background cross section is fitted by a Fano profile with and a width of a shape parameter q=-2.8438 7.549 x lo- I2au at a resonance energy of 0.2056 au. The double ionization energy is 33.92 eV compared to the measured value of 33.74 f 0.20 eV. The curve could be deepened slightly with a corresponding increase in the lifetime of the level and remain consistent with the measurements. A semi-classical analysis indicated that the empirical potential that we constructed may contain two resonances and indeed we located a second at an energy of 0.2333 au, just below the edge of the barrier, with a width corresponding to a lifetime of 2 x lo-l4 S.
Relined quanta1 calculations of the potential energy curve of the lowest ‘C + state of CH2+ are needed to confirm or reject our tentative identification of the doubly charged CH*+ ion observed by Mathur et al. [1,2]. Acknowledgement This work was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences. References [ I] D. Mathur, C. Badrinathan, F.A. Rajgara and U.T. Raheja, Chem. Phys. 103 (1986) 447.
[ 21 D. Mathur and C. Badrinathan, J. Phys. B20 (1987) 15 17. [3] J.A. Pople, B. Tidor and P. von R. Schleyer, Chem. Phys. Letters 88 (1982) 533. [4] T.G. Heil, SE. Butler and A. Dalgamo, Phys. Rev. A27 (1983) 2365. [ 5 I R.W. wetmore,R.K. Boyd and R.J. LeRoy, Chem. Phys. 89 (1984) 329. 161s. PrestonandA.Dalgamo,Chem.Phys. Letters 138 (1987) 157. [7] T.G. Heil, SE. Butler and A. Dalgamo, Phys. Rev. A 23 (1981) 1100.
471